Minahan, J. A.Nemeschansky, D.Vafa, C.Warner, N. P.2019-09-221998Minahan, J.A., D. Nemeschansky, C. Vafa, and N.P. Warner. 1998. “E-Strings and N = 4 Topological Yang-Mills Theories.” Nuclear Physics B 527 (3): 581–623. https://doi.org/10.1016/s0550-3213(98)00426-x.0169-68230550-32131873-1562http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385078We study certain properties of six-dimensional tensionless E-strings (arising from zero size E-8 instantons). In particular we show that n E-strings form a bound string which carries an E-8 level-n current algebra as well as a left-over conformal system with c = 12n - 4 - (248n/n + 30), whose characters can be computed. Moreover we show that the characters of the n-string bound state are captured by N = 4 U(n) topological Yang-Mills theory on 1/2K3. This relation not only illuminates certain aspects of E-strings but can also be used to shed light on the properties of N = 4 topological Yang-Mills theories on manifolds with b(2)(+) = 1. In particular the E-string partition functions, which can be computed using local mirror symmetry on a Calabi-Yau threefold, give the Euler characteristics of the Yang-Mills instanton moduli space on 1/2K3. Moreover, the partition functions are determined by a gap condition combined with a simple recurrence relation which has its origins in a holomorphic anomaly that has been conjectured to exist for N = 4 topological Yang-Mills on manifolds with b(2)(+) = 1 and is also related to the holomorphic anomaly for higher genus topological strings on Calabi-Yau threefolds.en-USJournal Article2019-09-2210.1016/S0550-3213(98)00426-X